1. Field of the Invention
The present invention is directed to an intraocular lens, and more particularly to an intraocular lens that corrects for the coma of the cornea.
2. Background
To aid in understanding this invention, a background of some basic optics fundamentals is provided below.
FIG. 1 shows a cross-section of a human eye 10. Under normal conditions, light rays 11 originating from an object 12 enter the eye 10 through the cornea 13, pass through a liquid known as the aqueous humor 14, pass through the iris 15, pass through the lens 16, pass through another liquid known as the vitreous humor 17, and form an image 18 on the retina 19.
The eye can suffer diseases that impair a patient's vision. For instance, a cataract may increase the opacity of the lens 16, causing blindness. To restore the patient's vision, the diseased lens may be surgically removed and replaced with an artificial lens, known as an intraocular lens, or IOL. A patient whose natural lens has been removed is said to have aphakia, and one who surgically receives an artificial lens is said to have pseudophakic vision.
In the absence of aberrations and diffraction, there is an essentially one-to-one correspondence between points on the object 12 and points on the image 18. FIGS. 2 and 3 show an example of aberration-free imaging, using a generic lens 21. The generic lens 21 is drawn as a simple two-surface lens, but is intended to represent the chain of optical elements in the eye, including the cornea 13 and the lens 16. An object 23 forms an image 24 on the retina 22. An on-axis bundle of rays 29 originating at the base 25 of the object 23 passes through the generic lens 21, and the rays strike the retina 22 at the base 27 of the image 24. Similarly, an off-axis bundle of rays 31 originating at the edge 26 of the object 23 passes through the generic lens 21, and the rays strike the retina 22 at the edge 28 of the image 24. In general, the visual acuity of the eye is directly related to the amount of aberration present in the eye's optical system, and any reduction in aberration is desirable.
An intraocular lens is typically corrected for a single focus, meaning that objects at a particular position away from the eye appear in focus, while objects at an increasing distance away from that position appear increasingly blurred.
This is illustrated in FIGS. 4 through 7. In FIGS. 4 and 5, a too-distant object 43, more distant from the generic lens 21 than object 23, forms an image 44 that is axially translated away from the retina 22 toward the lens 21. FIG. 4 shows an on-axis bundle of rays, and FIG. 5 shows an off-axis bundle of rays. In terms of aberrations, the optical system 40 in FIGS. 4 and 5 shows a positive amount of defocus.
A positive amount of defocus can occur even if the eye has its natural lens 16, if the range over which the natural lens 16 can accommodate is too small. When occurring with the natural lens 16, this condition is known medically as myopia, or nearsightedness, and can be remedied by spectacles or a contact lens that introduces negative optical power into the eye's optical system, thereby increasing the effective focal length of the system and axially translating the image 44 back toward the retina 22.
Similarly, in FIGS. 6 and 7, a too-close object 63, closer to the generic lens 21 than object 23, forms an image 64 that is axially translated away from the retina 22 away from the lens 21. Although the rays are drawn in FIGS. 6 and 7 as propagating beyond the retina to the image 64, in reality, the rays terminate at the retina 22 before forming an image. FIG. 6 shows an on-axis bundle of rays, and FIG. 7 shows an off-axis bundle of rays. In terms of aberrations, the optical system 60 in FIGS. 6 and 7 shows a negative amount of defocus.
When a negative amount of defocus occurs with the natural lens 16, it is known medically as hypermetropia, or farsightedness, and can be remedied by spectacles, a contact lens or a phakic lens that introduces positive optical power into the eye's optical system, thereby decreasing the effective focal length of the system and axially translating the image 64 back toward the retina 22.
For a single focal length IOL, a focal length is typically chosen to correct for relatively distant objects, and close objects appear as blurry without additional spectacles or contact lenses.
In addition to defocus, an intraocular lens can reduce astigmatism in the eye. Astigmatism occurs when the optical power along one axis differs from the optical power along a different axis, leading to a rotationally asymmetric wavefront. For instance, the optical power along a vertical axis may be envisioned by blocking all the light in the pupil of the eye except a thin vertical slice through the center of the lens. Similar situations hold for a horizontal axis, or any other orientation between vertical and horizontal. The astigmatism may be corrected by adding a cylindrical component of power to the IOL along a particular axis, so that the wavefront that strikes the retina is essentially rotationally symmetric. The correction of astigmatism is well-known, and is straightforwardly accomplished in IOLs, as well as spectacles and some contact lenses.
As a further improvement to an intraocular lens in which defocus and astigmatism are reduced, spherical aberration may be reduced. In general, for a lens that has a finite amount of spherical aberration, the optical power at the edge of the lens is different from the optical power at the center of the lens. A bundle of rays originating from a single point on the object, after passing through a lens with spherical aberration, does not converge to a single point on the image, but blurs by an amount in proportion to the amount of spherical aberration. FIG. 8 shows an optical system 80 with positive spherical aberration. For a lens 81 with positive spherical aberration, the edge of the lens has more optical power than the center of the lens. A bundle of rays 84 originating at the base of the object 83 passes through the aberrated lens 81, and does not come to a sharp focus at the retina 82. Rather, the rays passing through the edge of the lens 81 converge more quickly than the rays passing through the center of the lens 81, leading to a blur at the retina 82. Similarly, FIG. 9 shows an optical system 90 with negative spherical aberration, in which the lens 91 has less optical power at its edge than at its center. For a bundle of rays 94 originating from the base of the object 93 and passing through the aberrated lens 91, rays passing through the edge of the lens 91 converge less quickly than rays passing through the center of the lens 91, leading to a blur at the retina 92. In general, spherical aberration is rotationally symmetric about the optical axis. Spherical aberration is also independent of field height or field angle, so that a bundle of rays originating from the edge of the object would exhibit the same amount of spherical aberration as a bundle originating from the base.
There are known ways to reduce spherical aberration in IOLs. For instance, U.S. Pat. No. 6,609,793, incorporated by reference in its entirety herein, discloses a method of designing an ophthalmic lens. First, at least one of the surfaces of the cornea is characterized as a mathematical model. Then, the model is used to calculate the aberrations of the surface or surfaces. Finally, the lens is modeled to reduce the aberrations for at least one of the foci, for an optical system that includes the lens and at least one of the surfaces of the cornea. In particular, the publication discloses reducing to essentially zero the eleventh Zernike coefficient, which corresponds to third-order spherical aberration. Additional correction is disclosed in U.S. patent application Ser. No. 10/724,852, and U.S. Pat. No. 6,705,729, which are each herein incorporated by reference in their entirety.
In addition to spherical aberration, another wavefront aberration that degrades the image at the retina is coma. The general characteristics of coma are rotationally asymmetric, and are therefore difficult to draw in simple figures in the manner of exemplary FIGS. 2-9. Instead, a picture of an exemplary wavefront aberrated by coma is shown in FIG. 10. An observer located at the retina, looking at the lens, sees an aberrated wavefront 104 propagating toward him. For comparison, an unaberrated wavefront 103 is shown, superimposed on the aberrated wavefront 104. Along an axis 102, denoted by “x”, the two wavefronts 103 and 104 coincide. Along an axis 101, denoted by “y” and perpendicular to axis 102, the aberrated wavefront 104 shows an odd-order departure from the unaberrated wavefront 103. Third-order coma shows a cubic dependence in the wavefront departure along axis 101, fifth-order coma shows a fifth-order dependence, and so forth for higher odd-orders of coma. Although “x” and “y” are drawn as horizontal and vertical in FIG. 10, in reality the coma axes may have any orientation.
For a bundle of off-axis rays originating at a single point on the object, the rays converge to a cone-shaped blur at the image. Rays passing through the center of the aberrated lens arrive at the point of the cone, with the remainder of the bundle of rays filling out the characteristic cone shape. The orientation of the cone is radial with respect to the optical axis, and the size of the cone increases with distance away from the optical axis.
For a human eye 10 with good vision, the total amount of coma is generally fairly small. However, the cornea 13 and natural lens 16 may individually have substantial amounts of coma of opposite sign, which offset each other when light passes through both elements sequentially. When the natural lens 16 is removed and replaced with an IOL, the coma of the cornea 13 may become significant, so that if the cornea's coma is not corrected by the IOL, it may degrade the vision of the eye.
Accordingly, there exists a need for an intraocular lens that corrects for the coma of the cornea. When implanted, such an IOL reduces the amount of coma in the optical system of the eye (cornea and IOL together), and improves the vision of the eye.